
where \(\mu _y\)  is the centroid of all embeddings in class \(y\) .
The first term on the right hand side is exactly the regulariser in the center loss [1]}.
This may be interpreted as encouraging a more Gaussian distribution for the embeddings:
indeed,
\(& \sum \nolimits _{x \in S_y} \Vert  \Phi ( x ) - \mu _y \Vert _2^2 \\& = \sum \nolimits _{x \in S_y} -\log \mathsf {N}( \Phi ( x ); \mu _y, \sigma ^2_y I ) + \textrm {constant},\) 
